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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="group_1.html#L1" title="GROUP_1:struct.1">HGrStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font>;<br/>



<div><i><font color="Green" title="E8">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1"/><i><font color="Green" title="E9">A2</font></i>: 
<span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>consider </b><font color="Maroon" title="c3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c2">A</font>;<br/><b>consider </b><font color="Maroon" title="c4">g1</font>, <font color="Maroon" title="c5">g2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:16_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">g2</font>
 <b>and </b><br/><a NAME="E5:16_1"/><i><font color="Green" title="E10">A3</font></i>: 
<font color="Maroon" title="c4">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 <b>and </b><br/><a NAME="E6:16_1"/>
<font color="Maroon" title="c5">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>by </b><i><a class="txt" href="group_2.html#E1:16_1"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="group_2.html#T12" target="_self" title="GROUP_2:th.12">Th12</a></i>;<br/><b>thus </b><a NAME="E7:16_1"/>
contradiction
 <b>by </b><i><a class="txt" href="group_2.html#E5:16_1"><i><font color="Green" title="E10">A3</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_2"/><i><font color="Green" title="E9">A4</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/><b>consider </b><font color="Maroon" title="c3">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span>;<br/><b>consider </b><font color="Maroon" title="c4">g1</font>, <font color="Maroon" title="c5">g2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E4:16_2"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c5">g2</font>
 <b>and </b><br/><a NAME="E5:16_2"/>
<font color="Maroon" title="c4">g1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 <b>and </b><br/><a NAME="E6:16_2"/><i><font color="Green" title="E10">A5</font></i>: 
<font color="Maroon" title="c5">g2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="group_2.html#E1:16_2"><i><font color="Green" title="E9">A4</font></i></a>, <a class="ref" href="group_2.html#T12" target="_self" title="GROUP_2:th.12">Th12</a></i>;<br/><b>thus </b><a NAME="E7:16_2"/>
contradiction
 <b>by </b><i><a class="txt" href="group_2.html#E6:16_2"><i><font color="Green" title="E10">A5</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:16"/>
( <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="group_2.html#E1:16"><i><font color="Green" title="E8">A1</font></i></a></i>;<br/>


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